上海交通大学：《材料热力学》教学资源_07电子教案（英文课件）lecture 13 Solution II

Contents of Today S.J.T.U. Phase Transformation and Applications Review previous Non-ideal Solution Gibbs-Duhem Relation Integrating the Gibbs-Duhem Equation Dilute Solution and Colligative Properties Review of today SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 13 Solution Il

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 13 Solution II Contents of Today Review previous Non-ideal Solution Gibbs-Duhem Relation Integrating the Gibbs-Duhem Equation Dilute Solution and Colligative Properties Review of today

Introduction 2 S.J.T.U. Phase Transformation and Applications 相变是物质由一个相向另一个相的传递过程 扩散是物质由高浓度区向低浓度区的传递过程 化学反应可以看作是物质由反应物向产物的传递过程 在传递过程中化学势将起决定作用。 在恒温恒压下， dG=∑4，dn 再由自由能判据dG≤0可得判据的另一形式（化学势判据）： ∑4，dn,≤0 在相变过程中物质i总是由化学势高的一相向转向化学势低的 一相，直到两相中的化学势相等为止。而物质在两相中存在的 化学势差△μ；是物质传递的动力。 SJTU Thermodynamics of Materials Spring 2006 ©X.J.Jin Lecture 13 Solution Il

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 13 Solution II Introduction 2 在相变过程中物质i总是由化学势高的一相向转向化学势低的 一相，直到两相中的化学势相等为止。而物质在两相中存在的 化学势差 Δμ i 是物质传递的动力。 = ∑ i ii 在恒温恒压下， dG μ dn 再由自由能判据 dG≤0 可得判据的另一形式（化学势判据）： 相变是物质由一个相向另一个相的传递过程 扩散是物质由高浓度区向低浓度区的传递过程 化学反应可以看作是物质由反应物向产物的传递过程 在传递过程中化学势将起决定作用。 ∑ ≤ 0 i ii μ dn

例子 S.J.T.U. Phase Transformation and Applications 在等温等压下，两相平衡是常见的，如复相黄铜（铜一锌合 金)中o黄铜和β黄铜的平衡。设系统0、B两相相接触，在 等温等压下，若组分B(例如铜)有dn.由相进入B相，则o 相中B组分减少dng,而B相中B组分增加dng;其吉布斯函 数变化分别为： 0相 β相 dG=ug(-dnB) dGu(dng) 总的吉布斯函数变化等于 dG =dG+dG=(u-u)(dnB) SJTU Thermodynamics of Materials Spring 2006 ©X.J.Jin Lecture 13 Solution Il

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 13 Solution II 例子 在等温等压下，两相平衡是常见的，如复相黄铜(铜－锌合 金)中α黄铜和β黄铜的平衡。设系统α 、β两相相接触，在 等温等压下，若组分B（例如铜）有dnB由α相进入β相，则α 相中B组分减少dnB ，而β相中B组分增加dnB ；其吉布斯函 数变化分别为: )( dG −= dnBBαα μ )( dG dnBBββ = μ 总的吉布斯函数变化等于 ))(( dGdGdG dnBBB α αββ −=+= μμ α相 β相

例子续1 S.J.T.U. Phase Transformation and Applications 系统达到平衡时，即 dG 0 因为dnB≠0 所以 哈=8 上式表明，对于多组分多相系统的平衡条件是：“除系统中各 相的温度和压力必须相等外，任一组分在各相中的化学势也 必须相等。”即 4哈=4哈=…=哈 0相 B相 SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 13 Solution Il

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 13 Solution II 例子续1 系统达到平衡时，即 dG = 0 因为 dnB ≠ 0 所以 αβ = μμ BB 上式表明，对于多组分多相系统的平衡条件是：“除系统中各 相的温度和压力必须相等外，任一组分在各相中的化学势也 必须相等。”即 βα γ BB "=== μμμ B α相 β相

例子续2 S.J.T.U. Phase Transformation and Applications 若上述转移过程可以实现，则 0相 β相 dG=(uu)(dng)0 所以 哈<g 组分B有dn由o相 进入B相 上式表明物质总是由化学势较高的相自发转移到化学势较 低的相，直到该物质在两相中的化学势相等。 对比水与水位、电流与电势的关系，也有某种势的意思， 所以称为化学势 SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 13 Solution Il

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 13 Solution II 例子续2 上式表明物质总是由化学势较高的相自发转移到化学势较 低的相，直到该物质在两相中的化学势相等。 对比水与水位、电流与电势的关系，也有某种“势”的意思， 所以称为化学势 若上述转移过程可以实现，则 −= 0 αβ < μμ BB 组分B有dnB由α相 进入β相 α相 β相

化学势判据 S.J.T.U. Phase Transformation and Applications ∑4sdnB≤0 ∑4，d,≤0 这一判据式讨论具体的平衡规律、过程的方向与限度 SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 13 Solution ll

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 13 Solution II 这一判据式讨论具体的平衡规律、过程的方向与限度 ∑ ≤ 0 B μ dnBB 化学势判据 ∑ ≤ 0 i ii μ dn

P,V,Xi影响化学势 S.J.T.U. Phase Transformation and Applications 1,温度的影响 ∂G 298 =-S aT) ,xi 2,压力的影响 气相 aG RT =V L= dG=RTdln P aP P T,xi 3,组成的影响：偏摩尔Gibbs自由能 SJTU Thermodynamics of Materials Spring 2006 ©X.J.Jin Lecture 13 Solution Il

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 13 Solution II P, V, Xi影响化学势 S T G i xP ⎟ −= ⎠⎞ ⎜⎝⎛ ∂∂ , dT TC S P ∫ = 2980 0298 1，温度的影响 2，压力的影响 V P G i xT ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ , PRT V = 气相 = ln PRTdGd 3，组成的影响：偏摩尔Gibbs自由能

Thermodynamic activity S.J.T.U. Phase Transformation and Applications Fugacity is defined for gases: dGi=RTd(Infi) Thermodynamic activity of a component,i,is defined as: n0 The fugacity of the componentiin its standard state. The fugacity of a condensed phase is equal to the fugacity of the vapor phase in equilibrium with it. The fugacity of the vapor is equal to the pressure of the vapor,if the vapor in equilibrium with the condensed phase is ideal. SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 13 Solution Il

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 13 Solution II )(ln i i = fRTdGd D i i i f f α ≡ Thermodynamic activity Fugacity is defined for gases: Thermodynamic activity of a component, i, is defined as: D i f The fugacity of the component i in its standard state. The fugacity of a condensed phase is equal to the fugacity of the vapor phase in equilibrium with it. The fugacity of the vapor is equal to the pressure of the vapor, if the vapor in equilibrium with the condensed phase is ideal

Relative Partial Molar Quantities S.J.T.U. Phase Transformation and Applications Mixing of A and B to form a solution,the volume changes: AVmixing =VM =Vfimal -Vimitial VM is the volume change upon mixing: 混合前后容量性质变化 Vy =naVA+nBV B-naLa-nBLB Vy=na(VA-La)-nB(V8-LB) 网A-卫 The relative partial molar volume of A The partial molar volume of A in solution relative to the molar volume of pure A. -rel rel Vy =navA +nBVB SJTU Thermodynamics of Materials Spring 2006 ©X.J.Jin Lecture 13 Solution Il

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 13 Solution II Relative Partial Molar Quantities Δ mixing M == final −VVVV initial AM A B B A A BVnVnVnVnV B −−+= )()( AM A A B B VVnVVnV B −−−= rel B B rel AM A += VnVnV Mixing of A and B to form a solution, the volume changes: VM is the volume change upon mixing: A A −VV The relative partial molar volume of A The partial molar volume of A in solution relative to the molar volume of pure A. rel V A 混合前后容量性质变化

Relative Partial Molar Quantities (2) S.J.T.U. Phase Transformation and Applications M=n4F+nBF公 For one mole of solution, rel rel LM =XAVA +XBVB U,F,G,H,S,V The equations for variations of thermodynamic properties with temperature, pressure,and so on apply to solutions as well as to pure components. dGrl =-SredT G=GA-GA=RTInaA SJTU Thermodynamics of Materials Spring 2006 ©X.J.Jin Lecture 13 Solution Il

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 13 Solution II Relative Partial Molar Quantities (2) rel B B rel AM A += VnVnV rel B B rel M A A += VxVxV dTSGd rel rel −= A A A rel A =−= RTGGG lnα D For one mole of solution, U, F, G, H, S, V The equations for variations of thermodynamic properties with temperature, pressure, and so on apply to solutions as well as to pure components